Digital time signal filtering method and device for transmission channel echo correction

ABSTRACT

A method for filtering a time signal (e(t)) sampled in blocks of N samples (e(n),e(k)) uses a transfer function defined in the frequency domain by LN samples (H(K)). The transfer function is filtered by a time window (g1) of width N, and a frequency subsampling of ratio N is performed to give a partial transfer function defined over N samples (H1(k)). The method enables the complexity of circuits operating in real time to be optimized. The technique is particularly suitable for correcting long echoes in television picture receivers.

BACKGROUND OF THE INVENTION

The invention relates to a process for digitally filtering time signalssuch as those received from a transmission channel or a broadcastingnetwork.

It also relates to a digital filtering device for implementing theprocess.

The invention is particularly advantageous to realize echo correction atthe level of a receiver connected to a transmission system such as atelevision network.

Generally, digital filtering relates to a digital time signal, that is,one which results from a sampling at the rate of a given sampling periodT generally imposed in accordance with requirements that the processingallow for a determined bandwidth, for example. Thus a video signal inconformity with the D2-MAC standard, for example, is sampled for aperiod of 49.38 nanoseconds.

Digital filtering of such a signal can be performed in the frequencydomain, that is, from the discrete Fourier transform of the digital timesignal. In this case, the filtering is defined by a transfer functionwhich is also sampled at a given frequency sampling interval df. Thistransfer function, then is the sampled Fourier transform of the timeimpulse response of the filter to be produced.

Mathematically, the filtering consists of calculating, at each samplingperiod T, the convolution product of the time signal and the impulseresponse of the filter. In the time domain, the result of theconvolution produces the filtered signal directly. If the filter isdefined by its transfer function in the frequency domain, theconvolution is reduced to a simple product (in the complex space) of thediscrete Fourier transform of the time signal to be filtered by thetransfer function of the filter for each of the frequency values forwhich the transfer function is defined. The result of this complexproduct furnishes the discrete Fourier transform of the filtered signal.An inverse discrete Fourier transform makes it possible to return to thetime domain.

In order for this filter to be achievable in practice, the number ofsamplings in the time and frequency domains is obviously limited. Thisresults in conditions and limitations relative to the ranges ofdefinition for time and frequency quantities. Thus, in conformity withShannon's theorem, the time sampling at the period T imposes alimitation on the bandwidth of the signal which can be filtered. Thisfirst condition can be expressed by saying that the sampling frequency1/T of a real time signal must be more than double its bandwidth DF. Thesampling in the frequency domain also involves a second condition: thetime signal to be filtered is only taken into account during a limitedtime interval DT of a duration at most equal to the inverse 1/df of thesampling interval df in the frequency domain. The maximum interval 1/dfthus defines a time window which will henceforth be called the "timehorizon" of the filter.

The first of the preceding conditions is met by limiting the bandwidthof the time signal by means of filtering and/or by choosing a samplingfrequency 1/T which is high enough. The second condition will also bemet if the time signal can be represented by means of a limited numberof samplings processed by the filter at each sampling period.

If the discrete Fourier transform mentioned above is used, a limitednumber N of samplings in the time domain is used to calculate the samenumber N of samplings in the frequency domain. The two precedingconditions can therefore be summed up by the following relations:

    T≧1/(2 DF)                                          (1)

    df≧1/DT                                             (2)

    N.df≦2DF                                            (3)

    N.T≦DT                                              (4)

in which:

T is the time sampling period

df is the frequency sampling interval

N is the number of samplings used for the discrete Fourier transform

DF is the bandwidth of the time signal

DT is the time horizon of the filter.

A time signal filtering operation by means of a digital filter H issummarized in theory in FIG. 1, which shows the operations performed inthe time and frequency domains as well as the correspondences betweenone domain and the other. The upper part of the figure shows the varioustime parameters involved in the filtering, while the lower part showsthe corresponding parameters (by Fourier transform) in the frequencydomain.

Thus, the time signal e(t) to be filtered (assumed to be continuous) issampled at the period T and converted into a digital quantity by theconverter A/N which furnishes the sampled digital signal e(nT), in whichn is the rank of the corresponding sampling e(n). Since the filter H isassumed to be defined by its sampled impulse response h(n), thefiltering operation consists of calculating the convolution product:

    s(n)=h(n)*e(n)

The result of this convolution product furnishes the sampled output timesignal s(nT) of the filter. A digital-to-analog conversion N/A of thissignal makes it possible to obtain an analog output time signal s(t).

The same filtering in the frequency domain is represented in the lowerpart of the figure. The input signal E(f) is the transform of the timesignal e(t). This signal is sampled at a sampling interval df andconverted into a digital quantity by the converter A/N which furnishesthe sampled frequency signal E(k·df). As the filter H is assumed to bedefined in the frequency domain, the filtering operation consists ofobtaining the complex product of the samplings E(k·df) multiplied by thesamplings of the same rank k of the transfer function sampled in thefrequency domain H(k·df). The results of these products constitute theoutput sampled in the frequency domain S(k·df) of the filter. Adigital-to-analogue conversion N/A makes it possible to work in thecontinuous frequency domain instead.

As previously indicated, the practical realization of a time signalfiltering imposes a limitation on the number of samplings of the signalto be filtered and the transfer function which are involved in theoperations just described. FIG. 2 illustrates a conventional filteringcarried out in the frequency domain in which the number of samplings islimited to the value N. In this case, the continuous time signal e(t)appears in the form of a vector or block of samplings e(n)! obtained by,for example, a sampling at the period T followed by an analog-to-digitalconversion A/N and a serial-to-parallel conversion S-P which affects Nsuccessive samplings e(nT). Since the transfer function H of the filteritself is assumed to be sampled over N samplings, it also appears in theform of a block of samplings H(k)!. Strictly speaking, then, thefiltering consists of obtaining in parallel the products of thesamplings H(k) of the transfer function H multiplied by those of thesame rank E(k) which represent the discrete Fourier transform of thesampled time signals e(n). This discrete Fourier transform TFD operatesover N samplings e(n)! of the time signal and can be carried out bymeans of a circuit which uses an algorithm of the "fast Fouriertransform," or FFT, type. The products S(k) of the samplings E(k) timesH(k) define the discrete Fourier transform of the output time signals(n) which results from the filtering. The output time signal isobtained by means of an inverse discrete Fourier transform TFD⁻¹ whichoperates on each block of N products S(k)!. A parallel-to-serialconversion P-S at the rate of the sampling period T furnishes the timesignal S(t) at the instants t=nT.

It is certain that the complexity of the filter to be produced isdirectly linked to the size of the operators which execute the directand inverse discrete Fourier transforms, that is, to the number N ofsamplings processed by these operators. For example, it is possible todemonstrate that the number of multiplications necessary to produce afast Fourier transform of the size N is equal to N·log₂ (N). Thus, it isadvantageous to choose the smallest possible number N which iscompatible with the conditions (1) and (4) defined previously. It wouldbe desirable, however, for the sampling of the transfer function H ofthe filter to also satisfy conditions (2) and (3).

In the case in which the transfer function H used is defined in thefrequency domain with very high precision, that is, with a very largenumber of samplings H(K) separated by a very small frequency samplinginterval df, these samplings cannot be used directly since theconditions (1) through (4) would not generally be satisfied. In otherwords, this means that the time horizon 1/df of the filter defined byits transfer function H(K) is greater than the time horizon N·T. whichwould be sufficient to filter the signal. If it is assumed, for example,that the inverse 1/df of the sampling df of the transfer function H is amultiple L of the time horizon NT, the direct utilization of thesamplings H(K) would normally require discrete Fourier transforms of asize LN, which would make them uselessly oversized.

The problem, then, is the following. A transfer function H defined overa number L·N of samplings H(K) is used even though only N samplingswould be enough to filter time signal e(n). The object of the inventionis to find a filtering process which uses a transfer function H1 definedby N samplings H1(k) and which can represent the transfer function Hdefined by L·N samplings H(K) with sufficient precision.

SUMMARY OF THE INVENTION

In keeping with this object, the invention proposes a process for thefiltering by means of a transfer function of a digital time signalsampled at a sampling period T and represented by its discrete Fouriertransform defined by blocks of N samplings in the frequency domain, thistransfer function being sampled in the frequency domain and defined fora number LN of samplings, L being a whole number greater than or equalto 2, characterized in that, prior to the processing of the time signal,a partial transfer function is calculated which is defined in thefrequency domain by the following steps:

definition of a function in the time domain, called a time window, whichhas a value other than zero within a time interval of a duration equalto N times the sampling period T, and which assumes a value of zero ortending toward zero outside this interval,

calculation of the cyclic convolution product over LN samplings of thetransfer function sampled by the discrete Fourier transform of the timewindow,

subsampling of this convolution product in the ratio L in order todefine N samplings of the partial transfer function,

and in that the respective products of these samplings of the partialtransfer function multiplied by the samplings of the same rank of thediscrete Fourier transform of the time signal are obtained in real time.

It is advantageously possible to define the time window by means of afunction sampled in the time domain, and in this case, according toanother aspect of the invention, the cyclic convolution product consistsof carrying out a calculation of the inverse discrete Fourier transformof this sampled transfer function, obtaining the respective products ofthe samplings of the inverse discrete Fourier transform multiplied bythe samplings of the same rank of the sampled time window, andcalculating the discrete Fourier transform of these products.

In another aspect of the invention, the time window is chosen so thatits integral relative to time is equal to N times the sampling period T.

The process just defined actually makes it possible to adjust the timehorizon of the filter to that of the time signal to be filtered when theinitial transfer function H of the filter is defined too narrowly forthe requirements of the filtering. The result is an optimization of thesize and complexity of the discrete Fourier transform circuits (such asFFT and FFT⁻¹) which must function in real time. While still within theobject of reducing the size of these circuits, this problem is linked toa complementary problem which may be expressed as follows. A transferfunction, in the form of samplings with a given frequency samplinginterval df, is used. In order to filter a time signal, it is desirableto use discrete Fourier transforms of reduced size N, whereas the timehorizon of the signal which is normally necessary for filtering isgreater than NT but less than 1/df. It has already been seen how thetime horizon of the filter may be reduced. What now remains is to find apermanent solution which makes it possible to increase the time horizonwithout increasing the size N of the discrete Fourier transformcircuits.

Another subject of the invention is a filtering process which makes itpossible to solve this problem. More precisely, the invention relates toa process for the filtering by means of a transfer function of a digitaltime signal sampled at a sampling period T and represented by itsdiscrete Fourier transform defined by blocks of N samplings in thefrequency domain, this transfer function being sampled in the frequencydomain and defined for a number LN of samplings, L being a whole numbergreater than or equal to 2, characterized in that, prior to theprocessing of the time signal, M partial transfer functions arecalculated, which are defined in the frequency domain by the followingsteps:

definition of M successive time intervals, each having a duration equalto N times the sampling period T,

for each of these intervals, definition in the time domain of afunction, called a time window, which has a value other than zero withinthe associated time interval and which assumes a value of zero ortending toward zero outside this interval,

calculation of the cyclic convolution products over LN samplings of thesampled transfer function multiplied by the discrete respective Fouriertransforms of these time windows,

subsampling of these convolution products in the ratio L so as to defineN samplings of each of the partial transfer functions,

and in that the sum of partial frequency signals organized into M blocksof N samplings, which respectively result from the products of thesamplings of the M partial transfer functions multiplied by samplings ofthe same rank of M successive blocks of N samplings of this discreteFourier transform of the time signal is obtained in real time.

In a variant which makes use of the linear properties of the Fouriertransforms, the invention also relates to a process for the filtering bymeans of a transfer function of a digital time signal sampled at asampling period T and represented by its discrete Fourier transformdefined by blocks of N samplings in the frequency domain, this transferfunction being sampled in the frequency domain and defined for a numberLN of samplings, L being a whole number greater than or equal to 2,characterized in that, prior to the processing of the time signal, Mpartial transfer functions are calculated, which are defined in thefrequency domain by the following steps:

definition of M successive time intervals, each of which has a durationequal to N times the sampling period T,

for each of these intervals, definition in the time domain of afunction, called a time window, which has a value other than zero withinthe associated time interval and which assumes a value of zero ortending toward zero outside this interval,

calculation of the cyclic convolution products over LN samplings of thissampled transfer function multiplied by the respective discrete Fouriertransforms of these time windows,

subsampling of these convolution products in the ratio L so as to defineN samplings of each of the partial transfer functions

and in that the sum of partial frequency signals organized into M blocksof N samplings, which respectively result from M successive products ofthe samplings of the M partial transfer functions multiplied by thesamplings of the same rank of N samplings of the discrete Fouriertransform of the time signal.

Thus, the invention makes it possible to break down a defined transferfunction into any number of samplings in a bank of elementary filters,each of which is defined by a lower number of samplings. The result isthat the global complexity of the necessary circuits is lower than thatwhich would result from the direct utilization of the samplings of theinitial transfer function.

Another subject of the invention is the application of the filteringprocess just defined to echo correction in a transmission channel. Inthis case, the filtering affects a sampled digital time signal which ispresent at the level of a receiver connected to the transmissionchannel, this transfer function being determined from the calculation ofthe inverse of the transfer function in the frequency domain of thischannel.

Another subject of the invention is a digital filter for implementingthe process according to the invention. This filter is characterized inthat it includes a digital calculator programmed to calculate thesamplings of the partial transfer functions and equipped with an outputinterface which makes it possible to issue these samplings, and in thatthis filter includes hardwired circuits for calculating the discreteFourier transform of the time signal as well as the products of thesamplings of this partial transfer function multiplied by the samplingsof the same rank of the discrete Fourier transform of the time signal.

In the case of an embodiment in a filter bank, the filter according tothe invention is characterized in that it includes a digital calculatorprogrammed to calculate the samplings of the partial transfer functionsand equipped with an output interface which makes it possible to issuethese samplings, and in that this filter includes hardwired circuits forcalculating the discrete Fourier transform of the time signal, as wellas the products of the samplings of the partial transfer functionsmultiplied by the samplings of the same rank of the discrete Fouriertransform of the time signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, details of embodiment and advantages of the inventionwill appear in the remainder of the description, in reference to thefigures.

FIGS. 1 and 2 are schematic diagrams for introducing the various signalsused;

FIG. 3 is a schematic diagram of the process according to the invention;

FIG. 4 represents the principle elements which constitute the filteraccording to the invention;

FIG. 5 represents the elements of the filter bank according to theinvention for defining the partial transfer functions;

FIG. 6 represents diagrams which define the time windows used in thefilter bank in FIG. 5,

FIGS. 7 through 9 represent several variants of the embodiment of thefilter bank according to the invention;

FIG. 10 represents the clock signal used to synchronize the circuitrepresented in FIG. 9;

FIGS. 11 through 13 are diagrams which illustrate the application of thefilter according to the invention to echo correction in a transmissionchannel.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In order to facilitate comprehension of the rest of the explanations,the following conventional notations will be used:

L, M and N are integers, with M≧L;

the signals or transfer functions (impulse responses)

are in lower case when they are expressed in the time domain and inupper case in the frequency domain;

n or m designates the rank of the current sampling of a signal or animpulse response in the time domain, with o≧n≧N-1 and o≧m≧LN-1

k or K designates the rank of a current sampling of a signal or animpulse response in the frequency domain, with o≧1≧N-1 and o≧K≧LN-1;

the references between brackets designate blocks of samplings which havea size N or LN depending on whether they contain, respectively, the ranksymbols n, k or m, K.

FIGS. 1 and 2 have been used above to illustrate the differentquantities that are likely to be involved in a conventional digitalfiltering. In this case, the number N of samplings H(k) which definesthe transfer function H of the filter is equal to that of the samplingse(n) or e(k) of the time signal defined in the time or frequency domain.In order to restore this condition when a greater number LN of samplingsH(K) of the transfer function H defined in the frequency domain is used,according to the invention a processing of these samplings is carriedout in such a way as to define a new transfer function H1 represented byN samplings H1(k). This transform is illustrated in FIG. 3.

It consists first of all of defining in the time domain a time window g1which can be represented by a function which assumes the value 1 (with anear-scale coefficient) within a time interval of a duration equal to Ntimes the sampling period T. The convolution product of the sampledtransfer function H(K)! multiplied by the discrete Fourier transformG1(K))! of this time window g1 is calculated in order to obtain LNsamplings H1(K)!. Then a subsampling of H1(K)! in the ratio L is carriedout in order to obtain the desired transfer function H1 defined over Nsamplings H1(k). By applying these samplings H1(k)! to the input H(k)!of the filter represented in FIG. 2, the desired filtering of the timesignal e(t) defined over the time horizon NT is obtained.

FIG. 4 is an assembly diagram of one variant of the filter whichimplements the preceding process. The filter includes a circuit 1 forcalculating in real time the discrete Fourier transform defined byblocks E(k)! of N samplings of the time signal e(t) to be filtered. Thecircuit 1 includes an analogue-to-digital converter A/N which receivesthe continuous time signal e(t) and which is sequenced by a clock signalCK0 with the period T. The converter A/N furnishes, at each period T,the sampled signal e(n) applied to the input of a serial-to-parallelconverter S-P synchronized by a clock signal CK with the period NT insuch a way as to furnish blocks of N samplings e(n)!. By processing thisblock by means of a discrete Fourier transform circuit FFT-N of the sizeN, the discrete Fourier transform (E(k)! is obtained. Of course, thecircuit 1 would be superfluous if other means were used for thesamplings E(k).

FIG. 4 also shows one particular way to produce the convolution of theinitial transfer function H(K)! by means of the time window g1 definedpreviously. In this embodiment, the time window g1 is in the form of asampled function g1(m) defined over LN samplings in the time domain. Inthis case, the impulse response h(m)! of H(K)! is calculated by aninverse Fourier transform. For example, it is possible to use anoperator of the "inverse fast Fourier transform" type FFT-¹ -LN of thesize LN. This transform furnishes LN samplings h(m)! which aremultiplied by the samplings of the same rank in the time window g1(m)!.A Fourier transform FFT-LN of these products h1(m)! furnishes LNsamplings H1(K)!. As before, these samplings are subsamplings in a ratioL so as to furnish N samplings H1(k)!.

The circuit includes multipliers for obtaining, in parallel and in realtime, the products of the samplings H1(k) multiplied by the samplings ofthe same rank k of the discrete Fourier transform E(k) of the timesignal. These products furnish the samplings S1(k)! which constitute thediscrete Fourier transform of the output signal of the filter. Fromthese samplings S1(k)!, it is possible to obtain the sampled outputsignal in the time domain s(n) by means of an inverse discrete Fouriertransform FFT⁻¹ -N.

FIG. 5 represents a generalization of the preceding filter in the formof a filter bank which performs a breakdown of the initial transferfunction H(K) into M partial transfer functions H1, . . . , H4, . . .each of which is defined over N samplings, with M≧L. For this purpose, Mtime windows g1, g2, . . . , gM are defined, as represented in thediagram in FIG. 6. Each of these windows corresponds to a time horizonof a duration NT, and therefore the juxtaposition of M adjacent windowsmakes it possible to define a time horizon of a duration M.NT. It mustbe noted that the time windows are not necessarily rectangular windowsbut can also have the appearance represented in the diagram by a dottedline so that they project beyond both sides of the rectangular referencewindow while retaining the same surface area. This disposition makes itpossible, in particular, to avoid problems during the reconstruction ofthe output signal from the partial output signals obtained by thefiltering of the input time signal by the partial transfer functions H1,H2, . . . , HM.

The operations described in reference to FIGS. 3 and 4 are performed foreach of the levels of the filter bank.

Thus according to a first possibility, for each level, the cyclicalconvolution product of the transfer function H(K) multiplied by thediscrete Fourier transform G1(K), G4(K), . . . of the time window g1, .. . , g4, . . . of the level in question is calculated. In anotherpossibility, the convolution product is obtained by the calculation ofthe inverse discrete Fourier transform h(m) of the transfer functionH(K) followed by the calculation of the respective products h1(m), . . ., h4(m), . . . of the samplings h(m) multiplied by the samplings of thesame rank in each sampled time window g1(m), . . . , g4(m), . . .defined in the time domain. A calculation of the discrete Fouriertransform of these products h1(m), . . . , h4(m), . . . furnishes thesampling blocks H1(K)!, . . . , H4(K)!, .

As before, the samplings H1(K), . . . , H4(K), . . . are subjected to asubsampling of ratio L in order to furnish the desired partial transferfunctions H1(k), . . . , H4(k), . . . .

The partial transfer functions H1, . . . , H4, . . . can be used toreconstruct an output signal defined by blocks of only N samplings buttaking into account a time horizon greater than NT. The way to carry outthis reconstruction by means of a filtering cell will now be describedin reference to FIGS. 7 through 10.

In a first possibility represented in FIG. 7, the filtering cell 2constitutes M successive blocks of N samplings of the discrete Fouriertransform E(k)! by means of delay circuits connected to a shiftregister, for example. These delay circuits furnish at the output of theblocks shifted relative to one another by a time interval equal to NT. Mmultipliers obtain the products of the samplings of the partial transferfunctions H1(k)!, . . . , H4(k)!, . . . , times the samplings of thesame rank of the successive blocks which issue from the delay circuits.The multipliers furnish, at the output, M blocks of partial frequencysignals of N samplings S1(k)!, S4(k)!, . . . which are then added inparallel in an adder whose output furnishes N samplings of the discreteFourier transform S(k) of the output signal of the filter.

It is important to note that if M=L, a filtering is carried out over atime horizon of the input signal which is equal to the time horizon ofthe initial transfer function H(K).

FIG. 8 represents a second variant of the embodiment of the filteringcell 2 which is functionally equivalent to that in FIG. 7. These twoembodiments are distinguished from one another by the fact that theproducts and the delays are permutated.

In another variant represented in FIG. 9 which corresponds to an exampleof a filter bank with four levels, the delay and addition operations arealternated so that the addition of M blocks of samples is replaced by asuccession of additions of only two blocks each. This has the advantageof simplifying the embodiment of the adders and of consequently reducingthe calculation time.

The operation of the circuit in FIG. 9 is immediately apparent from thediagram and the timing diagram in FIG. 10, which show the sampling clocksignal CKO and the clock signal of the block CK used to synchronize thecircuit.

In order to illustrate a particularly advantageous application of thefiltering process according to the invention, FIG. 11 represents ageneral diagram of an example of a data transmission system, such as atelevision image transmission system.

In a conventional way, the system is constituted by an emitter 3, atransmission network 4, and a receiver 5. The receiver 5 is constitutedby the cascading of a demodulator 6, a low-pass filter 7, ananalog-to-digital converter 8 associated with an equalizer 9 andpossibly an echo correction filter H advantageously embodied accordingto the invention. The equalizer 9 is provided both for recovering theclock signal of the signal received and for producing a suppression ofthe so-called "short" echos which are inevitably produced throughout thetransmission channel Q.

However, the counterpart of the suppression of short echos by theequalizer 9 is the creation of so-called "long" echos which, althoughvery weak, are detrimental to the quality of the image. That is why itis useful to provide the supplementary filter H intended for suppressinglong echos. However, the processing of long echoes by definitionpresupposes that the filter H will have to account for a substantialtime horizon of the signal to be filtered. That is why the process andthe filter according to the invention are particularly well adapted tosolving this problem without the necessity of providing bulky filters.

FIG. 12 represents an embodiment of the assembly of the filter H whichis particularly useful for long echo correction. It is essentiallycomposed of a filtering cell 2 in conformity with the inventionconnected on one hand to a calculator 10, and connected to the inputsignal e(n)! by means of a fast Fourier transform circuit FFT-N. Thecalculator 10 receives the input signal in order to calculate thetransfer function Q of the channel from a sweep signal transmitted bythe emitter 3. The sweep signal allows the calculator to calculate withhigh precision the sampled transfer function in the frequency domain ofthe channel Q. The calculator can then calculate the inverse of thisfunction Q in order to obtain the transfer function of the filter Hafter a possible correction to assure the stability of the filter.Advantageously, the calculator 10 could use an adaptation algorithmwhich makes it possible to regularly adjust the coefficients of thetransfer function calculated. For example, line 624 of the signal D2-MACcould be used to transmit the sweep signal.

Finally, the calculator will be programmed to calculate the coefficientsof the partial transfer functions H1, . . . , H4, . . . in conformitywith the process according to the invention. Of course, if one transferfunction H1 would be sufficient, it would be possible to use the samecalculator with a cell 2 reduced to one multiplier. The opposite casewould make it necessary to provide M partial transfer functions andconsequently a cell 2 such that the product M.N.T. would be at leastequal to the length of the echo to be corrected.

As one exemplary embodiment, FIG. 13 shows the principal elements whichconstitute the calculator 10. The calculator is organized around a bus Bto which are connected a processor 11, a program memory 12, a firstmemory 13 for containing the samplings WOB(n) of the sweep signal and asecond memory 14 provided for containing the calculated coefficients ofthe filter H as well as the partial transfer functions Hi. An inputinterface IE and an output interface IE enable the bus B to communicatewith the input signal e(n)! and the multipliers of the filtering cell 2,respectively.

Since the calculator just described is the conventional type, itsdetailed constitution and its operation do not require supplementaryexplanations, taking into account the indications already given above.

This mixed embodiment, which combines a programmed calculator 10 forcalculating the coefficients with hardwired circuits for processing thesignal in real time, seeks to optimize production costs while satisfyingthe performance criteria.

We claim:
 1. A process for the filtering by means of a transfer function (H) of a digital time signal ((e(n))) sampled at a sampling period T and represented by its discrete Fourier transform ((E(k))) defined by blocks of N samplings in the frequency domain, said transfer function (H) being sampled ((H(K))) in the frequency domain and defined for a number LN of samplings, L being a whole number greater than or equal to 2, characterized in that, prior to the processing of the time signal ((e(n))), a partial transfer function ((H1(k))) is calculated which is defined in the frequency domain by the following steps:definition of a function in the time domain, called a time window (g1), which has a value other than 0 within a time interval of a duration equal to N times the sampling period T, and which assumes a value of zero or tending toward zero outside said interval, calculation of the cyclic convolution product ((H1(K))) over LN samplings of said sampled transfer function ((H(K))) by the discrete Fourier transform ((G1(K)) of said time window (g1), subsampling of said convolution product ((H1(K))) in the ratio 1/L in order to define N samplings of said partial transfer function ((H1(k))), and multiplying said samplings of said partial transfer function ((H1(k))) by the samplings of the same rank of said discrete Fourier transform ((E(k))) of said time signal ((e(n))) to obtain respective products ((S1(k))) in real time in order to produce an output signal corrected for channel echo introduced by a transmission channel over which an input signal corresponding to the digital time signal ((e(n))) has passed.
 2. The filtering process according to claim 1, characterized in that said time window (g1) being a sampled function, said cyclic convolution product ((H1(k))) consists of carrying out a calculation of the inverse discrete Fourier transform ((h(m))) of said sampled transfer function ((H(K))), obtaining the respective products ((h1(m))) of the samplings of said inverse discrete Fourier transform ((h(m))) multiplied by the samplings of the same rank of said sampled time window (g1), and calculating the discrete Fourier transform ((H1(K))) of said products ((H1(m))).
 3. The filtering process according to claim 1, characterized in that said time window (g1) is chosen so that its integral relative to time is equal to N times the sampling period T.
 4. An application of the filtering process according to claim 1 to echo correction in a transmission channel, characterized in that the filtering affects a sampled digital time signal which is present at the level of a receiver connected to said transmission channel, said transfer function (H) being determined from the calculation of the inverse of the transfer function (Q) in the frequency domain of said channel.
 5. The application of the filtering process according to claim 4, characterized in that said transfer function of the channel is determined by means of a sweep signal produced by an emitter connected to the other end of said channel.
 6. A digital filter for implementing the filtering process according to claim 1, characterized in that it includes a digital calculator programmed to calculate said samplings of said partial transfer function (H1(k)) and equipped with an output interface which makes it possible to issue said samplings, and in that said filter includes hardwired circuits for calculating said discrete Fourier transfer (E(k)) of the time signal (e(n)) as well as the product of said samplings of said partial transfer function (H1(k)) multiplied by the samplings of the same rank of the discrete Fourier transform (E(k)) of the time signal (e(n)).
 7. A process for the filtering by means of a transfer function (H) of a digital time signal (e(n)) sampled at a sampling period T and represented by its discrete Fourier transform ((E(k))) defined by blocks of N samplings in the frequency domain, said transfer function (H) being sampled ((H(K)) in the frequency domain and defined for a number LN of samplings, L being a whole number greater than or equal to 2, characterized in that, prior to the processing of the time signal, M partial transfer functions ((H1(k))), . . . , ((H4(k))) are calculated, which are defined in the frequency domain by the following steps:definition of M successive time intervals, each having a duration equal to N times the sampling period T, for each of said intervals, definition in the time domain of a function, called a time window, (g1, . . . , g4) which has a value other than zero within the associated time interval and which assumes a value of zero or tending toward zero outside said interval, calculation of the cyclic convolution products ((H1(K)), . . . , (H4(K))) over LN samplings of said sampled transfer function multiplied by the respective discrete Fourier transforms ((G1(K)), . . . , (G4(K))) of said time windows (g1, . . . , g4), subsampling of said convolution products ((H1(K)), . . . , (H4(K))) in the ratio 1/L so as to define N samplings of each of said partial transfer functions ((H1(k)), . . . , (H4(k))), multiplying said M partial transfer functions ((H1(k)), . . . , (H4(k))) by samplings of the same rank of M successive blocks of N samplings of said discrete Fourier transform ((ER(k))) of the time signal ((e(n)))to obtain partial frequency signals, summing the partial frequency signals organized into M blocks of N samplings in real time in order to produce an output signal corrected for channel echo introduced by a transmission channel over which an input signal corresponding to the digital time signal ((e(n))) has passed.
 8. The filtering process according to claim 7, characterized in that each of said time windows is chosen in such a way that its integral relative to time is equal to N times the sampling period T, so that the sum of two adjacent time windows is equal to unity.
 9. The application of the filtering process according to claim 7 for echo correction in a transmission channel, characterized in that said digital time signal (e(n)) is a signal which is present at the level of a receiver connected to one end of said channel, in that said transfer function (H) is the inverse of the transfer function (Q) of said channel, in that said M time intervals are adjacent and in that the numbers N and M are chosen in such a way that the product M.N.T. is at least equal to the length of the echo to be corrected.
 10. A digital filter for implementing the filtering process according to claim 7, characterized in that it includes a digital calculator programmed to calculate said samplings of said partial transfer functions (H1(k)) and equipped with an output interface which makes it possible to issue said samplings, and in that said filter includes hardwired circuits for calculating said discrete Fourier transform (E(k)) of the time signal (e(n)) as well as the products of said samplings of said partial transfer functions (H1(k)) multiplied by the samplings of the same rank of the discrete Fourier transform (E(k)) of the time signal (e(n)).
 11. A process for the filtering by means of a transfer function (H) of a digital time signal ((e(n))) sampled at a sampling period T and represented by its discrete Fourier transform ((E(k))) defined by blocks of N samplings in the frequency domain, said transfer function (H) being sampled ((H(K))) in the frequency domain and defined for a number LN of samplings, L being a whole number greater than or equal to 2, characterized in that, prior to the processing of the time signal ((e(n))), M partial transfer functions ((H1(k)), . . . , (H4(k))) are calculated, which are defined in the frequency domain by the following steps:definition of M successive time intervals, each of which has a duration equal to N multiplied by the sampling period T, for each of said intervals, definition in the time domain of a function, called a time window (g1, . . . , g4), which has a value other than zero within the associated time interval and which assumes a value of zero or tending toward zero outside said interval, calculation of the cyclic convolution products ((H1(K)), . . . , (H4(K))) over LN samplings of said sampled transfer function ((H(K)) multiplied by the respective discrete Fourier transforms ((G1(K)), . . . , (G4(K))) of said time windows (g1, . . . , G4), subsampling of said convolution products ((H1(K)), . . . , (H4(K))) in the ratio 1/L so as to define N samplings of each of said partial transfer functions (H1(k)), . . . , H4(k))), obtaining M successive products of the samplings of said M partial transfer functions (H1(k), . . . , (H4(k))) multiplied by the samplings of the same rank of N samplings of said discrete Fourier transform (E(k))) of the time signal ((e(n)), thus obtaining partial frequency signals, and summing in real time the partial frequency signals organized into M blocks of N samplings ((S1(k), . . . , S4(k))), in order to produce an output signal corrected for channel echo introduced by a transmission channel over which an input signal corresponding to the digital time signal ((e(n))) has passed.
 12. The filtering process according to claim 11, characterized in that said time windows (g1, . . . , g4) being sampled functions, each of said cyclic convolution products (H1(k)) consists of carrying out a calculation of the inverse discrete Fourier transform (h(m)) of said sampled transfer function (H(K)), obtaining the respective products (h1(m)) of the samplings of said inverse discrete Fourier transform (h(m)) multiplied by the samplings of the same rank in each of said sampled time windows (g1), and calculating the discrete Fourier transform (H1(K)) of said products (h1(m)). 